Finite Group Databasebeta

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C4⋊C4×#4318 #14751767

order2816
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4⋊C4×#4318

Splittings

SylowC11 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C4⋊C4×M16
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

1242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 167562);